Phase-based Optical Flow.
Phase-based optical flow can track constant phase contours by computing the phase gradient of a spatio-temporally bandpassed video. This can provide an approximation to the motion field, and shows that phase is more robust than amplitude in detecting image changes due to contrast and scale. A similar technique computes the temporal gradient of the phases of a spatially bandpassed video to estimate the motion field.
Complex Steerable Pyramids.
Steerable pyramids, which can be viewed as extensions of Laplacian pyramids, are over complete representations of images that decompose the images along scale and orientation. The basis functions are similar to Gabor wavelets, which are sine curves multiplied by a smooth spatial envelope.
A steerable pyramid can be real-valued by having all real coefficients, but it can be extended to complex-valued coefficients where the sine curves of basis functions are replaced by a complex exponential. In other words, the real part represents an even-symmetric filter (cosine), while its imaginary counterpart represents an odd-symmetric filter (sine). While the real and imaginary parts increase the over completeness of the representation, the complex-valued steerable pyramid is a richer representation that separates the amplitude of the local wavelet from its phase.